Reduce to lowest terms: $- \dfrac{8}{7} \div - \dfrac{7}{5} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{7}{5}$ is $- \dfrac{5}{7}$ Therefore: $ - \dfrac{8}{7} \div - \dfrac{7}{5} = - \dfrac{8}{7} \times - \dfrac{5}{7} $ $ \phantom{- \dfrac{8}{7} \times - \dfrac{5}{7}} = \dfrac{-8 \times -5}{7 \times 7} $ $ \phantom{- \dfrac{8}{7} \times - \dfrac{5}{7}} = \dfrac{40}{49} $